Vibration analysis of ring stiffened truncated conical shells under the influence of stationary and flowing fluids

Thin shells are extensively used in various modern industrial structures, such as aircraft fuselages, ship hulls, and the walls of nuclear containment vessels. In particular, conical shells play a crucial role in the design of numerous aerospace vehicles, from fighter jet fuel tanks to satellite launchers. As a result, understanding their vibrational and aeroelastic behaviors is key in their design. To enhance their sti˙ness, these shells are often reinforced with rings or stringers. This reinforcement, prevalent in the aerospace industry, involves adding sti˙eners either inside, outside, or on both sides of the shell. Research into the mechanical performance of these sti˙ened conical shells focuses on di˙erent types of sti˙eners - helical, longitudinal, and circumferential. These enhancements notably improve the shell’s load-bearing capacity without substantially increasing its weight, and also alter its static and dynamic properties, especially in shells that are vacuum or contain static or flowing fluids. Various shell theories, such as those by Donnell, Sanders, and Novozhilov, have been devel-oped to better understand these dynamics. They mainly di˙er in their assumptions about the strain-displacement relationship on the shell’s mid-surface. Sanders’ theory, for example, uses precise “small-strain” equations for membrane strains and linearized equations for reference-surface curvature and torsions changes. These theories help in deriving the equilibrium and motion equations for shells, and one common approach to discretize these equations is the Finite Element Method (FEM). FEM stands out for its adaptability in managing di˙erent boundary conditions. The presence of fluid near a shell significantly influences its dynamic behavior and can lead to structural damage due to fluidelastic instability. Understanding the dynamic properties of these structures in the presence of stationary or flowing fluid is thus critically important. This thesis aims to examine the linear vibration and predict buckling onset in truncated con-ical shells. It first develops a hybrid FEM formulation based on Sanders’ first-approximation theory for thin shells. The motion equations for shells are then derived using generalized coordinates and linear shell theories, with these coordinates represented by the shell’s nodal displacement. The interaction between the structure and stationary or flowing fluid is mod-eled using the Bernoulli equation, with fluid pressure e˙ects also represented in terms of nodal displacements.